Canada's famously low levels of productivity and low rates of productivity growth have preoccupied Canadian economists for decades. But increased productivity - as it is usually measured - is not a sufficient condition for higher standards of living. It's not even necessary. For instance, the post-2001 fall in Canadian productivity is simply a mathematical artifact of an income-increasing sectoral reallocation of capital and labour.
Gérard Debreu was once asked why he titled his landmark monograph Theory of Value instead of something like the more usual Price Theory. His answer was "Because value equals price times quantity." And this is the point: increasing quantities increases the value of production only if prices hold steady, or at least don't fall too much. But if prices are falling, increasing productivity won't necessarily show up as higher income.
Yi = AiFi(Ki,Li)
- Yi is output in industry i
- Ki is capital employed in industry i
- Li is labour employed in industry i
- Fi() is a function describing how capital and labour inputs are transformed into output
- Ai is a measure of the state of technology.
The model can be generalised to include more than two inputs, and Statistics Canada does so when calculating its estimates. Technical change is interpreted as changes in Ai. For a fixed level of inputs, an increase of 10% in Ai will increase output by 10%.
From the standard theory of the firm, wages are set equal to the marginal revenue product, which is the amount of extra revenue generated by an extra unit of labour:
wi = Pi Ai FLi(Ki,Li)
where FLi is he derivative of Fi with respect to the labour input Li. Wages will increase if
- Ai increases: Technical progress increases worker productivity and real wages.
- Ki increases: For a given level of technology, 'capital deepening' (usually) increases worker productivity and wages.
- Pi increases: Higher prices are passed on to workers. (Yes, really.)
In developing economies - such as China - you can produce significant gains in productivity and wages by just by accumulating capital. But at some point, diminishing returns set in, and growth stagnates without technical progress.
It's surprisingly easy to recover the growth rate of Ai, and Statistics Canada (see here for the gory details) publishes its estimates in Cansim tables 383-0021 and 383-0022. Here are a couple of graphs from those tables:
These measures are cyclical, falling during recessions: a reduction in capacity utilisation rates shows up as a fall in productivity. But even so, an increase in business sector MFP of just over 10% in the span of almost 50 years is still not particularly impressive. And business sector MFP has fallen over the past ten years.
Part of the explanation is the Baumol Effect: technical progress in the services sector is slower - or at least, harder to measure - than in the good sector, so the shift to services brought down average productivity growth. If we take the MFP estimates seriously, there has been no technical progress in the service sector since 1961.
But this is only part of the explanation. Here is a graph of the MFP for two important components of the goods sector:
Here is where one's faith in MFP starts to falter. Whatever MFP is measuring in the mining, oil and gas extraction sector, it cannot possibly be technical progress. No-one would seriously claim that output in this sector would be tripled if they returned to 1960s-era technology. It's much more easy to believe that technical change in this sector takes the form of making it possible to extract resources that were previously unreachable.
This MFP artifact appears to be driving the fall in goods sector MFP since 2001. If resources are shifted out of the manufacturing sector and towards the resource sector, aggregate MFP measures will fall. For a given level of labour and capital, a reallocation that reduced aggregate MPF will produce a lower level of GDP.
Everything else being equal, lower GDP means lower income. But everything else has not been equal. As we know from my old beer-and-pizza post, an increase in the terms of trade can increase incomes, even if output as measured by GDP stays constant. This recent StatsCan paper provides an overview of the distinction between GDP, Gross Domestic Income (GDI) and Gross National Income (GNI). (Fun fact: the old GNP measure is now called GNI. Am I the last to know this?)
This distinction is not as well-known as it might be, quite possibly because up until recently, it really didn't matter which measure you used. But the post-2001 increase in the prices of oil and other commodities have produced an unprecedented gap between GDP and GDI:
Here is a plot of the ratio of the industrial price index to the Bank of Canada's commodity price index:
Since 2001, the ratio of resource and manufacturing MFPs has fallen by one-third. But if relative prices of resources with respect to manufactured goods have doubled, then shifting away from manufacturing to resources will still increase incomes.
When we think about productivity, output is the implicit measure for economic welfare: more output means more income. But this only works if prices are held constant. Large increases in quantities multiplied by even larger reductions in prices reduces value. Making more of something people don't want to buy doesn't guarantee prosperity.